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%I #10 Aug 14 2024 08:34:35
%S 31,229,397,439,457,499,601,643,691,727,739,811,919,997,1021,1051,
%T 1093,1327,1459,1657,1699,1753,1933,1999,2113,2179,2203,2251,2281,
%U 2341,2347,2383,2671,2731,2767,2791,2833,2953,2971,3061,3229,3259,3331,3373,3391
%N Primes p such that x^3 = 2 has more than one solution mod p and the sum of the (three) solutions is p.
%C Subsequence of A040028 and of A014752, complement of A059914 relative to A014752. Solutions mod p are represented by integers from 0 to p-1.
%H Robert Israel, <a href="/A059899/b059899.txt">Table of n, a(n) for n = 1..10000</a>
%p filter:= proc(p) local S;
%p if not isprime(p) then return false fi;
%p S:= map(t -> rhs(t[1]), [msolve(x^3=2,p)]);
%p nops(S) = 3 and convert(S,`+`) = p
%p end proc:
%p select(filter, [seq(i,i=7..5000, 6)]); # _Robert Israel_, Aug 13 2024
%Y Cf. A040028, A014752, A059914.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Mar 02 2001